1 PHYS 414: Homework 6 This homework due Wednesday March 7 1. A Carnot engine is connected to thermal reservoirs at temperatures T 2 and T 1 through two identical thermal resistors R. [The heat current J passing through a thermal resis-tor R connecting two points diﬀering in temperature by Δ T is given by J = Δ T/R .] (a) (2 points) At what output power P does the engine have its maximum possible eﬃciency? (b) (2 points) What is the maximum possible eﬃciency that this engine could have? (c) (2 points) What is the maximum possible output power P that can be extracted using this engine? (d) (2 points) What is the eﬃciency η of this engine when it is producing the maximum possible power? (e) (2 points) At what rate is entropy being created by this engine when it is producing the maximum possible power? 2. (6 points) An evacuated container of volume V is initially thermally isolated from its surroundings, and is initially at temperature T0 , which is neither very small nor very large. The container has negligible heat capacity, so the heat energy of the system

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